Croatia moved off the foot of qualifying Group 5 but it took a late penalty by Ante Vukušić to earn his side their first victory of the campaign at the expense of Estonia.
It was a welcome return to winning ways for a side that had succumbed to three successive defeats and if confidence had been knocked by recent results they did not show it.
Their play was marked by quick passing and extensive use of the flanks. For all their domination, however, Ivan Šušak's side took 45 minutes to produce a genuine goal threat, Marcelo Brozović missing the target from close range after being picked out by Duje Čop's right-wing cross. Seconds before the interval, Croatia again came close, Ivan Lendrić denied by goalkeeper Marko Meerits after racing clear.
With Estonia sitting deep and posing the occasional threat on the break, the onus was on the visitors to make all the running, but when Čop's first-time strike from 12 metres was repelled by the excellent Meerits, it seemed their goalless run would stretch to a fourth match.
However, a minute from time, substitute Vukušić was hauled down by Aleksei Jahhimovitš and the 20-year-old HNK Hajduk Split striker scored from the ensuing penalty.